Question

For a closed organ pipe three successive resonance frequencies are observed at $425Hz,595Hz$ and $765Hz$ respectively. If the speed of sound in air is $340m/s,$ then the length of the pipe is :

• A. $2.0m$
• B. $0.4m$
• C. $1.0m$
• D. $0.2m$

Answer 1

Answer: (C)

$1.0m$

$\text{Given}:$ v = 340m/s, Ratio of 3 frequencies = 425 : 595 : 765

$\text{Solution}:$

Since frequencies are in odd number ratio , the pipe has to be a closed pipe.

Ratio of 3 frequencies = 425 : 595 : 765 = 5 : 7 : 9

So fundamental frequency

$=f=\frac{425}{5}=85Hz$

For fundamental frequency

$l=\frac{v}{4f}=\frac{340}{4\times 85}=1m$

$\text{Hence C is the correct option}$